In this paper, the analogy between electrical and mechanical quantities is reviewed. Based on this analogy, there is a missing link between displacement and momentum. This missing link corresponds to the link between the charge and flux which represents the memristor. This link is still missing between the mechanical quantities. In this work, we shed the light on this missing mechanical element. We introduce the mathematical relation which links displacement and momentum. Two main types of missing relations are discussed. © 2015 IEEE.

This paper introduces the design procedure for the low pass filter based on Chebyschev polynomials of fractional power of any order. The filter order is considered in intervals of width two. Only the first two intervals are considered along with their pole locus produced by varying the filter order and the magnitude response. A general formula for constructing the filter from its s-plane poles is suggested. Numerical analysis and circuit simulations using MATLAB and Advanced Design System (ADS) based on the proposed design procedure are presented. Good matching between the circuit simulation

The analysis of nonlinear fractional-order circuits is a challenging problem. This is due to the lack of nonlinear circuit theorems and designs particularly in the presence of memristive elements. The response of a series connection of a simple resistor with fractional order capacitor and its analytical formulation in both charging and discharging phases is considered. The numerical simulation of fractional order HP memristor in series with a fractional order capacitor is also discussed. It is a demonstration of a simple nonlinear fractional-order memristive circuit in both charging and

An analysis of a traditional rectifier circuit when a fractional-order capacitor with order 0 < α < 1 replaces the integer-order smoothing capacitor (α = 1) is presented. Exploring the change in discharging behaviour that results from this replacement and the impacts on ripple voltage, nominal DC voltage, current, and power expressions used to describe the performance of this class of circuits. Further, the assumptions made for the analysis of the traditional circuit are explored from the fractional perspective to determine if they are still valid. © 2016 IEEE.

The generation of Multi-scroll chaotic attractors and chaos theory has gained much attention due to its many usages in a wide range of applications such as image-encryption and random number generators. There have been many previous attempts to establish a system that is able to generate large numbers of n - scroll chaotic attractors by modifying existing systems such as Lorenz and Chua's systems. In this paper, a proposed system based on generalizing Chua's system that has shown its ability to produce an unprecedentedly large number of even and odd chaotic scrolls is introduced. MATLAB

The response of a commercial super-capacitor to an applied periodic current excitation in the form of a triangular waveform is investigated in this study. This waveform has a linear-with-time variation which enables linear charging and discharging of the device. A model consisting of a linear resistance Rs and a constant phase element is used to describe the super-capacitor impedance and expressions for the voltage across the device, the power, and stored energy are derived using concepts from fractional calculus. Experimental results are shown and an application of the study to super

In the recent decades, applications of chaotic systems have flourished in various fields. Hence, there is an increasing demand on generalized, modified and novel chaotic systems. In this paper, we combine the general equation of jerk-based chaotic systems with simple scaled discrete chaotic maps. Numerical simulations of the properties of two systems, each with four control parameters, are presented. The parameters show interesting behaviors and dependencies among them. In addition, they exhibit controlling capabilities of the ranges of system responses, hence the size of the attractor diagram

In this paper, we discuss the optimal charging and discharging of supercapacitors to maximize the delivered energy by deploying the fractional and multivariate calculus of variations. We prove mathematically that the constant current is the optimal charging and discharging method under R s -CPE model of supercapacitors. The charging and round-trip efficiencies have been mathematically analyzed for constant current charging and discharging. © 2020 The Electrochemical Society ("ECS"). Published on behalf of ECS by IOP Publishing Limited.

DC electrical voltage-current measuring instrument and data are an instrument used to measure the current and voltage generated by wind turbines and record the measurement results. The function of this instrument is to activate the dummy load on the wind turbine control system to reduce the voltage that exceeds the safe limit when saving electrical energy. The research aimed to manufacture and analyze DC electrical voltage - current measuring instrument using the Arduino Uno based data logger, capable of measuring the DC and voltage generated by Hybrid Power Plants (PLTH) and use the metrology

Chaos theory has attracted the interest of the scientific community because of its broad range of applications, such as in secure communications, cryptography or modeling multi-disciplinary phenomena. Continuous flows, which are expressed in terms of ordinary differential equations, can have numerous types of post transient solutions. Reporting when these systems of differential equations exhibit chaos represents a rich research field. A self-excited chaotic attractor can be detected through a numerical method in which a trajectory starting from a point on the unstable manifold in the